Norway · Grade 12 · Practice Sheet 37

1. 1.

   Find the population standard deviation of: 16, 20, 15, 4, 11 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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2. 2.

   Find the momentum of a 47 kg object moving at 14 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   kr 3,200 is invested at 6% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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4. 4.

   Two masses 6,200 kg and 810 kg are 13 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

   Formula:Newton’s Law of Gravitation

   $F = G\dfrac{m_1 m_2}{r^2}$

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5. 5.

   kr 2,500 is invested at 8% compound interest per annum for 3 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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6. 6.

   A body starts at 19 m/s and accelerates at 4.1 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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7. 7.

   A force of 11 N moves an object 10 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the population standard deviation of: 8, 16, 3, 4, 4 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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9. 9.

   A current of 2.1 A flows through a 30 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    Find the sum of the first 5 terms of a geometric series with first term a = 8 and common ratio r = 3.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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11. 11.

    Find the gravitational potential energy of a 25 kg object raised 20 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    Find the force needed to accelerate a 32 kg mass at 4.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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14. 14.

    A cone has base radius 8 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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15. 15.

    Two masses 7,200 kg and 180 kg are 8 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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16. 16.

    A device runs at 141 V drawing 6.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the momentum of a 51 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    Find the gravitational potential energy of a 16 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A population of 6,000 grows 8% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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20. 20.

    Find the force needed to accelerate a 43 kg mass at 0.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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